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Mathematics Magazine

Volume 84, 2011 - Issue 3
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Original Articles

Blood Vessel Branching: Beyond the Standard Calculus Problem

John A. Adam Department of Mathematics & Statistics, Old Dominion University jadam@odu.eduView further author information
Pages 196-207
Published online: 22 Dec 2017
 
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Original Articles

Blood Vessel Branching: Beyond the Standard Calculus Problem

Summary

Summary

Calculating the optimal angle for blood vessel branching is a standard calculus problem. However, optimality in that setting is judged by a cost functional that turns out not to give realistic results. We study a sequence of improvements to the cost functional, finally arriving at one that passes an important modeling test: From this last functional, we derive three empirical laws of blood vessel branching, originally proposed by German zoologist Wilhelm Roux.

This article is part of the following collections:
Carl B. Allendoerfer Prize: 2010s

Additional information

Notes on contributors

John A. Adam

JOHN A. ADAM is Professor of Mathematics at Old Dominion University in Norfolk, VA. His research interests are currently associated with theoretical problems in meteorological optics. He enjoys nature photography (of the point-and-shoot kind), and is a frequent contributor to the Earth Science Picture of the Day website (http://epod.usra.edu/). He is author of Mathematics in Nature: Modeling Patterns in the Natural World and coauthor of Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin (both Princeton University Press). His most recent book, A Mathematical Nature Walk (also Princeton) was published in June 2009. He enjoys being a grandparent of four small children: the geometric mean of their ages is 1.19 years (at the time of writing).

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